R Notebook
#packages
Housing Data Summary
House Pricing is the most intrinsic factor of economy, and they are of great interest for buyers and sellers. Moreover, nowadays housing price and property taxes is increasing rapidly and it is an important factor that needs to be considered, before purchasing a house because it is a long - term investment. From the survey of 2007 and 2008, it was found that many people bought the house on the basis of assumptions that housing price and property price will decrease in year 2007 and considering that factor, they took the loan from the bank and invested into properties, but that was not the case and this recession impacted many financial statements of individuals. Thus, the goal of the project is to build a regression model that would help to determine the factors that would lead to increase in housing price in different divisions and states.My aim is to focus on model which predict the Property Taxes on the basis of divisions, states, insurance, bathroom, kitchen and many more factors. This will give consciousness to individuals about the considerations of factors that needs to be taken before buying or selling house.
Methodology
Moreover,from ACS housing data I have filtered some columns which includes State,Division, Acres,Tax, Agro Products sales, Bath, Kitchen, Rent of house,and other household utilites which will help me to find the prediction of house before buying. I had similarly done this project in Foundation of Modelling in which we need to analyze some reserach paper on the basis of some topic. So, I decided to go with the Housing data in R and apply some research methods on it. In the research paper,they had simply cleaned the data and applied linear regression model on it, but in my project I tried to do some tests on it and also performed different reltion, which can help individual in buying housing property.
Therefore, I have performed different steps to identify regression model. 1st step: Loading and filtering data 2ndstep: Weighted mean of Monthly Rent and Insurance 3rd step: Labelling factors for better understanding 4th step: Performing different graphs for understanding relationship 5th step: Applied some tests on it 6th step: Checking AIC and Bic, to see which model fits better 7th step: Splitting data into train and test data 8th step: Building Linear Regression Model 9th step: Predicting model by using test data 10th step: Visualizing summary of model
fields <- c("RT", "DIVISION","ADJHSG", "ST","WGTP",
"ACR","AGS","BATH","BDSP", "HOTWAT",
"INSP","RMSP", "SINK","STOV","TEL",
"TOIL","VALP","YBL", "KIT","TAXP",
"RNTP")
A <- data.frame(fread
("C:/Users/Janvi/Documents/R/Final Project/csv_hus/psam_husa.csv",
header=TRUE,select = fields))
B <- data.frame(fread
("C:/Users/Janvi/Documents/R/Final Project/csv_hus/psam_husb.csv",
header=TRUE,select = fields))
C <- data.frame(fread
("C:/Users/Janvi/Documents/R/Final Project/csv_hus/psam_husc.csv",
header=TRUE,select = fields))
D <- data.frame(fread
("C:/Users/Janvi/Documents/R/Final Project/csv_hus/psam_husd.csv",
header=TRUE,select = fields))
bind_data <- rbind(A,B,C,D)
bind_data <- bind_data %>%
rename("RecordType" = RT,"DIVISION"= DIVISION,
"Adjacent Factor" = ADJHSG,"State" = ST,
"Housingweight" = WGTP,"HouseAcre" = ACR,
"SaleofAgroProduct"= AGS,"Bathtub" = BATH,
"Bedrooms" = BDSP,"HotWater" = HOTWAT,
"Insurance" = INSP,"Stove" = STOV,
"TelephoneService" = TEL,"Toilet" = TOIL,
"PropertyValue" = VALP,"HouseStructureYear" = YBL,
"Kitchen" = KIT,"Tax" = TAXP,"MonthlyRent" = RNTP)
View(bind_data)Weighted mean and labelling factors
In this section I have weighted monthy rent by adjacent factor to result it into dollars, then I have done same for the Insurance. Furthermore, I have labelled the factors of state, year built in and divisions.In the end of this chunk I have omitted the Na values and based upon that I have performed different relation of graphs.
#Weighted monthly rent
bind_data["RENT"]=bind_data["Adjacent Factor"]*bind_data["MonthlyRent"]/1000000
###Weighted mean of Insurance
bind_data["INSURANCE"]=bind_data["Adjacent Factor"]*bind_data["Insurance"]/1000000
#Labeling factors of DIVISION
bind_data$DIVISION <- factor(bind_data$DIVISION,
levels = c(1,2,3,4,5,6,7,8,9),
labels = c("New England", "Middle Atlantic",
"East North Central",
"West North Central",
"South Atlantic",
"East South Central",
"West South Central",
"Mountain","Pacific"))
bind_data$HouseStructureYear <- factor(bind_data$HouseStructureYear,
levels = c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21),
labels = c("1939 or earlier","1940 to 1949",
"1950 to 1959",
"1960 to 1969",
"1970 to 1979",
"1980 to 1989",
"1990 to 1999",
"2000 to 2004",
"2005","2006","2007",
"2008","2009","2010",
"2011","2012","2013",
"2014",
"2015",
"2016 ",
"2017"))
#Labeling states
bind_data$State <- factor(bind_data$State,
levels = c(1,2,4,5,6,8,9,
10,11,12,13,15,16,17,18,
19,20,21,22,23,24,25,26,27,
28,29,30,31,32,33,34,35,36,
37,38,39,40,41,42,44,45,
46,47,48,49,50,51,53,54,
55,56,72),
labels =
c("AL","AK","AZ","AR","CA","CO","CT","DE",
"DC","FL","GA","HI","ID","IL","IN","IA",
"KS","KY","LA","ME","MD","MA","MI","MN",
"MS","MO","MT","NE","NV","NH","NJ","NM",
"NY","NC","ND","OH","OK","OR","PA","RI",
"SC","SD","TN","TX","UT","VT","VA","WA",
"WV","WI","WY","PR"))
##Removing NA from data
Without_NA <- bind_data %>% select(State,DIVISION,Bathtub,HotWater,Bedrooms,RMSP,SINK,Stove,Toilet,
HouseStructureYear,Kitchen,RENT) %>% group_by(RENT) %>% na.omit()
head(Without_NA)Plotting Divisions by 2017 year wise
From the below graph we can see that number of houses built in South Atlantic are around 400 in year 2017 and least were built in New England, so the consumption of lands in New England is less, so we can predict that, rent in that division would be less. Moreover, when we tried that relation with omitted NA values then west south central shows highest built houses in year 2017, which is wrong prediction and thus by omitting NA can change a lot of result.
#Analysing Divisions Rent in 2017 year
year_division_bind <- bind_data %>%
select(DIVISION,Bathtub,RMSP,HouseStructureYear,RENT) %>%
filter(HouseStructureYear == 2017) %>%
group_by(DIVISION) %>%
summarise(Count=n())
year_division_bind#plot
ggplot(year_division_bind)+
geom_col(mapping =aes(x= DIVISION,y= Count,fill=DIVISION))+
ggtitle("Number of houses built in different divisions in year 2017")+
xlab("DIVISIONS")+ylab("Number of houses built")+ theme_bw()+
theme(plot.title= element_text(color="#0033FF",hjust = 0.5),
axis.text.x = element_text(angle = 90),
legend.position= "bottom")
#Analysing Divisions Rent in 2017 year by omitting NA
year_division <- Without_NA%>%
select(DIVISION,Bathtub,RMSP,HouseStructureYear,RENT) %>%
filter(HouseStructureYear == 2017) %>%
group_by(DIVISION) %>%
summarise(Count=n())
year_division#plot
ggplot(year_division)+
geom_col(mapping =aes(x= DIVISION,y= Count,colour =
DIVISION,fill=DIVISION))+
ggtitle("Division wise House count built in year 2017 With omitted NA") +
xlab("DIVISIONS")+ylab("Number of houses built")+ theme_bw()+
theme(plot.title= element_text(color="#0033FF",hjust = 0.5),
axis.text.x = element_text(angle = 90),legend.position =
"bottom")
Rent vs Division in year 2017
The below graph represents that average Rent of houses built in year 2017 were high in New England and least were in Mountain and East North Central, so investors can easily buy their houses on basis of rent.Moreover, in this graph when I tried with atual data without omitted NA value than I saw that there was no difference, so here I used data with omitted value to visualize data in better way.
#Plotting rent ,division wise in year 2017
rent_year <- Without_NA %>%
select(DIVISION,Bathtub,RMSP,HouseStructureYear,RENT) %>%
filter(HouseStructureYear == 2017 ) %>%
group_by(DIVISION) %>% summarise(Avg_rent=mean(RENT))
rent_year#Plot
ggplot(rent_year)+
geom_col(aes(x= DIVISION,y= Avg_rent,colour = DIVISION,fill=Avg_rent))+
ggtitle("Rent of houses built in different divisions in year 2017")+
xlab("DIVISIONS")+ylab("Rent of houses in year 2017 ")+
theme_bw()+
theme(plot.title= element_text(color="#0033FF",hjust = 0.5),
axis.text.x = element_text(angle = 90),
legend.position = "bottom")
## Total Rent in different states
From the below graph we can see that Hawaii(HW) of United states consist highest average Rent in comaprison to other states, thus this graph helps buyers to predict that they should not invest in hawaii if their financial statement is quite low, rather than that they should invest their income in west virgina and Arkansas.
#Total rent in different states
rent_rooms <- Without_NA %>%
select(State,RMSP,HouseStructureYear,RENT)%>%
group_by(State) %>% summarise(Avg_Rent= mean(RENT))
rent_rooms#Plot
ggplot(rent_rooms)+
geom_col(mapping =aes(x= State,y=Avg_Rent,colour = State,fill=State))+
ggtitle("Total Rent In Different States")+
xlab("States")+ylab("Total Rent Of Houses ")+theme_bw()+
theme(axis.text.x = element_text(angle = 90))
Houses built in different years
From the below graph, we can say that the ratio of houses built in early years were high compare to 2017, so we can say that houses built in recent years are less.
YR_division <- Without_NA%>%
select(RENT,DIVISION,HouseStructureYear)
YR_division#plot
options(scipen = 999)
ggplot(YR_division)+geom_bar(mapping =aes(x= DIVISION ,colour =
DIVISION,fill=DIVISION))+ facet_wrap(~HouseStructureYear)+
ggtitle("Number of houses built in different divisions")+
xlab("DIVISIONS")+ylab("Number of houses built")+theme_bw()+
theme(plot.title= element_text(color="#0033FF",hjust = 0.5),
axis.text.x = element_text(angle = 90))
## Tax in different divisions Here from below graph we can see that, tax in South Atlantic is highest and lowest in New England.
So, from overall graphs we can say that it is beneficial to built or rent a house in New England, as it contains lowest price by considering taxes and rent factors.
tax_division <- bind_data %>%
select(RENT,DIVISION,HouseStructureYear,Tax)
tax_division#plot
options(scipen = 999)
ggplot(tax_division)+geom_bar(mapping =aes(x= Tax ,colour =
DIVISION,fill=DIVISION))+facet_wrap(~DIVISION)+
ggtitle("Tax in different divisions")+
xlab("DIVISIONS")+ylab("Taxes")+theme_bw()+
theme(plot.title= element_text(color="#0033FF",hjust = 0.5),
axis.text.x = element_text(angle = 90),legend.position =
"bottom")
## Sale of Agriculture product in different division
Below graph depicts that East North Central has the highest tax on sale of agriculture products, so if any one wants to do business of agriculture products, they can easily depict from this graph information from where they can get benefit.Moreover, 300000 tax need to pay yearly by East North central which is costly for many individuals.
AGS_division <- bind_data %>%
select(SaleofAgroProduct,DIVISION,Tax) %>% group_by(Tax)
AGS_division#plot
ggplot(AGS_division)+
geom_col(aes(x=DIVISION,y=SaleofAgroProduct,fill=DIVISION))+
ggtitle("Sale of Agriculture products in different divisions")+
xlab("DIVISIONS")+ylab("SaleofAgroProduct")+
theme(axis.text.x = element_text(angle = 90),legend.position = "bottom")+
theme_bw()
Performing Various test for testing P value
From the below performed test we can depict that P value will remain below 0.05, which states that there is significance difference between them, thus it rejects null hypothesis and states that difference of mean of Sale of agro products and tax is not equal to 0 and thus we accept alternative hypothesis.
(Variance_test <- var.test(bind_data$SaleofAgroProduct,bind_data$Tax))##
## F test to compare two variances
##
## data: bind_data$SaleofAgroProduct and bind_data$Tax
## F = 0.002636, num df = 1199657, denom df = 4284627, p-value <
## 0.00000000000000022
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.002629336 0.002642677
## sample estimates:
## ratio of variances
## 0.002635994(Variance_test <- var.test(bind_data$HouseAcre,bind_data$Tax))##
## F test to compare two variances
##
## data: bind_data$HouseAcre and bind_data$Tax
## F = 0.00082329, num df = 5317320, denom df = 4284627, p-value <
## 0.00000000000000022
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.0008221860 0.0008243909
## sample estimates:
## ratio of variances
## 0.0008232881(t.test(bind_data$SaleofAgroProduct,bind_data$Tax,data=bind_data))##
## Welch Two Sample t-test
##
## data: bind_data$SaleofAgroProduct and bind_data$Tax
## t = -3366.7, df = 4364301, p-value < 0.00000000000000022
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -32.63092 -32.59295
## sample estimates:
## mean of x mean of y
## 1.275661 33.887593#Intial model of linear regression for checking AIC and BIC
By checking AIC and BIC we can say that int_model fits best as it has lowest AIC value. From the below image we can say that, the black colour in image means it has not included few variables in that area and the coloured area represents that they are related to log probablity.The log posterior probablity are scaled so 0 represents to lowest probablity from other models.
#Intial model of linear regression
int_model <- lm(Tax ~ State+DIVISION+ HouseAcre+ SaleofAgroProduct+
Bathtub+ HotWater+ Bedrooms+ RMSP+ SINK+ Stove+ Toilet+
HouseStructureYear+ Kitchen, data = bind_data)
summary(int_model)##
## Call:
## lm(formula = Tax ~ State + DIVISION + HouseAcre + SaleofAgroProduct +
## Bathtub + HotWater + Bedrooms + RMSP + SINK + Stove + Toilet +
## HouseStructureYear + Kitchen, data = bind_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -85.051 -9.225 -0.782 8.735 75.005
##
## Coefficients: (9 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) -11.978632 0.379278 -31.583
## StateAK 18.871273 0.322099 58.588
## StateAZ 16.630868 0.158068 105.213
## StateAR 5.818015 0.137528 42.304
## StateCA 30.540127 0.113192 269.808
## StateCO 15.790298 0.152607 103.470
## StateCT 47.127950 0.143027 329.504
## StateDE 10.332911 0.318478 32.445
## StateDC 20.907547 1.167119 17.914
## StateFL 18.281802 0.116580 156.818
## StateGA 13.209778 0.108751 121.468
## StateHI 16.465641 0.394057 41.785
## StateID 12.692697 0.193388 65.633
## StateIL 30.728808 0.122727 250.383
## StateIN 13.116626 0.124381 105.456
## StateIA 21.676571 0.159162 136.192
## StateKS 19.855180 0.167534 118.514
## StateKY 8.979579 0.127559 70.395
## StateLA 0.944223 0.139470 6.770
## StateME 24.142636 0.151454 159.406
## StateMD 31.233741 0.144384 216.324
## StateMA 42.071630 0.132679 317.093
## StateMI 20.482386 0.105622 193.922
## StateMN 19.033727 0.113131 168.245
## StateMS 4.828923 0.135862 35.543
## StateMO 12.753821 0.121243 105.192
## StateMT 17.648650 0.198275 89.011
## StateNE 23.154042 0.213143 108.632
## StateNV 16.530729 0.265788 62.195
## StateNH 45.060684 0.159561 282.405
## StateNJ 48.632161 0.146157 332.739
## StateNM 9.494139 0.189757 50.033
## StateNY 34.938775 0.106024 329.537
## StateNC 13.709460 0.108465 126.396
## StateND 8.127721 0.248994 32.642
## StateOH 24.089539 0.111405 216.233
## StateOK 8.427966 0.135393 62.248
## StateOR 24.318865 0.156491 155.401
## StatePA 26.995960 0.104242 258.974
## StateRI 44.161726 0.304737 144.917
## StateSC 5.897253 0.126294 46.695
## StateSD 17.018325 0.249335 68.255
## StateTN 9.615002 0.112887 85.174
## StateTX 22.133082 0.102664 215.588
## StateUT 13.537420 0.225218 60.108
## StateVT 39.553941 0.195003 202.837
## StateVA 16.754747 0.117946 142.054
## StateWA 28.891947 0.132081 218.745
## StateWV 5.338476 0.170191 31.368
## StateWI 30.288909 0.109925 275.542
## StateWY 13.949802 0.298105 46.795
## DIVISIONMiddle Atlantic NA NA NA
## DIVISIONEast North Central NA NA NA
## DIVISIONWest North Central NA NA NA
## DIVISIONSouth Atlantic NA NA NA
## DIVISIONEast South Central NA NA NA
## DIVISIONWest South Central NA NA NA
## DIVISIONMountain NA NA NA
## DIVISIONPacific NA NA NA
## HouseAcre 0.259257 0.037336 6.944
## SaleofAgroProduct 0.439793 0.015068 29.187
## Bathtub -3.311064 0.387065 -8.554
## HotWater NA NA NA
## Bedrooms 2.145049 0.018499 115.954
## RMSP 1.763974 0.007283 242.213
## SINK 3.099082 0.466792 6.639
## Stove 5.086451 0.389413 13.062
## Toilet 0.176973 0.003599 49.177
## HouseStructureYear1940 to 1949 0.915040 0.084415 10.840
## HouseStructureYear1950 to 1959 3.114449 0.067330 46.256
## HouseStructureYear1960 to 1969 3.415948 0.063914 53.446
## HouseStructureYear1970 to 1979 3.425114 0.054510 62.835
## HouseStructureYear1980 to 1989 5.104416 0.055662 91.704
## HouseStructureYear1990 to 1999 6.215056 0.053168 116.895
## HouseStructureYear2000 to 2004 8.684713 0.061854 140.406
## HouseStructureYear2005 9.855163 0.109661 89.870
## HouseStructureYear2006 10.196022 0.112380 90.728
## HouseStructureYear2007 10.493042 0.119794 87.592
## HouseStructureYear2008 10.375215 0.134688 77.031
## HouseStructureYear2009 10.071803 0.160769 62.648
## HouseStructureYear2010 9.775719 0.167285 58.437
## HouseStructureYear2011 10.165844 0.205380 49.498
## HouseStructureYear2012 9.864334 0.199505 49.444
## HouseStructureYear2013 10.777305 0.219550 49.088
## HouseStructureYear2014 10.649474 0.246261 43.245
## HouseStructureYear2015 10.357083 0.288970 35.841
## HouseStructureYear2016 8.878885 0.414538 21.419
## HouseStructureYear2017 7.995912 0.879378 9.093
## Kitchen -7.904206 0.362184 -21.824
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## StateAK < 0.0000000000000002 ***
## StateAZ < 0.0000000000000002 ***
## StateAR < 0.0000000000000002 ***
## StateCA < 0.0000000000000002 ***
## StateCO < 0.0000000000000002 ***
## StateCT < 0.0000000000000002 ***
## StateDE < 0.0000000000000002 ***
## StateDC < 0.0000000000000002 ***
## StateFL < 0.0000000000000002 ***
## StateGA < 0.0000000000000002 ***
## StateHI < 0.0000000000000002 ***
## StateID < 0.0000000000000002 ***
## StateIL < 0.0000000000000002 ***
## StateIN < 0.0000000000000002 ***
## StateIA < 0.0000000000000002 ***
## StateKS < 0.0000000000000002 ***
## StateKY < 0.0000000000000002 ***
## StateLA 0.00000000001288 ***
## StateME < 0.0000000000000002 ***
## StateMD < 0.0000000000000002 ***
## StateMA < 0.0000000000000002 ***
## StateMI < 0.0000000000000002 ***
## StateMN < 0.0000000000000002 ***
## StateMS < 0.0000000000000002 ***
## StateMO < 0.0000000000000002 ***
## StateMT < 0.0000000000000002 ***
## StateNE < 0.0000000000000002 ***
## StateNV < 0.0000000000000002 ***
## StateNH < 0.0000000000000002 ***
## StateNJ < 0.0000000000000002 ***
## StateNM < 0.0000000000000002 ***
## StateNY < 0.0000000000000002 ***
## StateNC < 0.0000000000000002 ***
## StateND < 0.0000000000000002 ***
## StateOH < 0.0000000000000002 ***
## StateOK < 0.0000000000000002 ***
## StateOR < 0.0000000000000002 ***
## StatePA < 0.0000000000000002 ***
## StateRI < 0.0000000000000002 ***
## StateSC < 0.0000000000000002 ***
## StateSD < 0.0000000000000002 ***
## StateTN < 0.0000000000000002 ***
## StateTX < 0.0000000000000002 ***
## StateUT < 0.0000000000000002 ***
## StateVT < 0.0000000000000002 ***
## StateVA < 0.0000000000000002 ***
## StateWA < 0.0000000000000002 ***
## StateWV < 0.0000000000000002 ***
## StateWI < 0.0000000000000002 ***
## StateWY < 0.0000000000000002 ***
## DIVISIONMiddle Atlantic NA
## DIVISIONEast North Central NA
## DIVISIONWest North Central NA
## DIVISIONSouth Atlantic NA
## DIVISIONEast South Central NA
## DIVISIONWest South Central NA
## DIVISIONMountain NA
## DIVISIONPacific NA
## HouseAcre 0.00000000000382 ***
## SaleofAgroProduct < 0.0000000000000002 ***
## Bathtub < 0.0000000000000002 ***
## HotWater NA
## Bedrooms < 0.0000000000000002 ***
## RMSP < 0.0000000000000002 ***
## SINK 0.00000000003157 ***
## Stove < 0.0000000000000002 ***
## Toilet < 0.0000000000000002 ***
## HouseStructureYear1940 to 1949 < 0.0000000000000002 ***
## HouseStructureYear1950 to 1959 < 0.0000000000000002 ***
## HouseStructureYear1960 to 1969 < 0.0000000000000002 ***
## HouseStructureYear1970 to 1979 < 0.0000000000000002 ***
## HouseStructureYear1980 to 1989 < 0.0000000000000002 ***
## HouseStructureYear1990 to 1999 < 0.0000000000000002 ***
## HouseStructureYear2000 to 2004 < 0.0000000000000002 ***
## HouseStructureYear2005 < 0.0000000000000002 ***
## HouseStructureYear2006 < 0.0000000000000002 ***
## HouseStructureYear2007 < 0.0000000000000002 ***
## HouseStructureYear2008 < 0.0000000000000002 ***
## HouseStructureYear2009 < 0.0000000000000002 ***
## HouseStructureYear2010 < 0.0000000000000002 ***
## HouseStructureYear2011 < 0.0000000000000002 ***
## HouseStructureYear2012 < 0.0000000000000002 ***
## HouseStructureYear2013 < 0.0000000000000002 ***
## HouseStructureYear2014 < 0.0000000000000002 ***
## HouseStructureYear2015 < 0.0000000000000002 ***
## HouseStructureYear2016 < 0.0000000000000002 ***
## HouseStructureYear2017 < 0.0000000000000002 ***
## Kitchen < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.54 on 1073351 degrees of freedom
## (6413930 observations deleted due to missingness)
## Multiple R-squared: 0.4489, Adjusted R-squared: 0.4489
## F-statistic: 1.107e+04 on 79 and 1073351 DF, p-value: < 0.00000000000000022int_model1 <- lm(Tax ~ Bathtub+HotWater+Bedrooms+RMSP+
SINK+Stove+Toilet+HouseStructureYear+
Kitchen,data = bind_data)
# Checking which one is better AIC or BIC,Lower the value,
#better the model fits
(aic_model <- AIC(int_model,k=2))## [1] 8792634(aic_model <- AIC(int_model1,k=2))## [1] 37260276(bic_model <- BIC(int_model))## [1] 8793596(bic_model <- BIC(int_model))## [1] 8793596#value of AIC model is less so AIC is considered optimal for int_model
model_BAS <- bas.lm(log(Tax) ~ HouseAcre+SaleofAgroProduct
+Bathtub+HotWater+SINK+Stove+Toilet+Kitchen,
data = bind_data, prior = "AIC", modelprior=uniform(),
method = "MCMC", MCMC.iterations=500000)
summary(model_BAS)## P(B != 0 | Y) model 1 model 2
## Intercept 1.000000 1.0000 1.0000000
## HouseAcre 0.999748 1.0000 1.0000000
## SaleofAgroProduct 0.999998 1.0000 1.0000000
## Bathtub 0.999986 1.0000 1.0000000
## HotWater 0.000000 0.0000 0.0000000
## SINK 0.806194 1.0000 0.0000000
## Stove 0.999958 1.0000 1.0000000
## Toilet 0.999984 1.0000 1.0000000
## Kitchen 1.000000 1.0000 1.0000000
## BF NA 1.0000 0.2482373
## PostProbs NA 0.8061 0.1937000
## R2 NA 0.0047 0.0047000
## dim NA 8.0000 7.0000000
## logmarg NA -7438376.5647 -7438377.9580651
## model 3 model 4
## Intercept 1.0000000000 1.00000000000
## HouseAcre 0.0000000000 0.00000000000
## SaleofAgroProduct 1.0000000000 1.00000000000
## Bathtub 1.0000000000 1.00000000000
## HotWater 0.0000000000 0.00000000000
## SINK 1.0000000000 0.00000000000
## Stove 1.0000000000 1.00000000000
## Toilet 1.0000000000 1.00000000000
## Kitchen 1.0000000000 1.00000000000
## BF 0.0003073404 0.00007148497
## PostProbs 0.0001000000 0.00010000000
## R2 0.0047000000 0.00470000000
## dim 7.0000000000 6.00000000000
## logmarg -7438384.6522496780 -7438386.11071831919
## model 5
## Intercept 1.00000000000000000000
## HouseAcre 0.00000000000000000000
## SaleofAgroProduct 1.00000000000000000000
## Bathtub 1.00000000000000000000
## HotWater 0.00000000000000000000
## SINK 0.00000000000000000000
## Stove 0.00000000000000000000
## Toilet 1.00000000000000000000
## Kitchen 1.00000000000000000000
## BF 0.00000000000002643981
## PostProbs 0.00000000000000000000
## R2 0.00459999999999999992
## dim 5.00000000000000000000
## logmarg -7438407.82860064785927534103image(model_BAS, rotate = F)
Splitting Train and Test data
I am making train data with 75% of train data and rest 25% are test data.
set.seed(99)
split <- sample(seq_len(nrow(bind_data)), size = floor(0.75 * nrow(bind_data)))
train <- bind_data[split, ]
test <- bind_data[-split, ]Building Linear Regression Model
I am predicting tax by considering different factors such as state, division, bathtub, sale of agro product and etc, by taking train data. The summary description is explained after result of summary model.
model2 <- lm(Tax ~ State+DIVISION+HouseAcre+SaleofAgroProduct+
Bedrooms+RMSP+HouseStructureYear+SINK+Bathtub+
Kitchen+INSURANCE, data=train)
(summary(model2))##
## Call:
## lm(formula = Tax ~ State + DIVISION + HouseAcre + SaleofAgroProduct +
## Bedrooms + RMSP + HouseStructureYear + SINK + Bathtub + Kitchen +
## INSURANCE, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71.138 -8.379 -0.863 7.662 69.059
##
## Coefficients: (8 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) -12.20285590 0.35251582 -34.616
## StateAK 17.69582778 0.35623286 49.675
## StateAZ 17.18290632 0.17311286 99.258
## StateAR 5.82044765 0.14997625 38.809
## StateCA 28.01200988 0.12695324 220.648
## StateCO 13.74604994 0.17356931 79.196
## StateCT 45.52747842 0.16602066 274.228
## StateDE 11.70148306 0.34629368 33.791
## StateDC 19.89317605 1.27809000 15.565
## StateFL 14.95310148 0.13316932 112.286
## StateGA 13.16824537 0.11899211 110.665
## StateHI 14.08507248 0.45394278 31.028
## StateID 14.19249331 0.20932087 67.803
## StateIL 30.31831190 0.13395611 226.330
## StateIN 12.76131462 0.13546385 94.205
## StateIA 21.88632363 0.17362596 126.054
## StateKS 18.10230146 0.18915859 95.699
## StateKY 8.85557620 0.13947921 63.490
## StateLA -0.22691249 0.15644730 -1.450
## StateME 25.16245457 0.16303181 154.341
## StateMD 31.39316073 0.15967069 196.612
## StateMA 40.91579165 0.14866974 275.213
## StateMI 21.15973149 0.11516788 183.729
## StateMN 17.68805415 0.12521623 141.260
## StateMS 3.99551931 0.15021201 26.599
## StateMO 11.81095063 0.13359312 88.410
## StateMT 17.18363440 0.21975790 78.193
## StateNE 22.19599338 0.23814842 93.202
## StateNV 16.99405118 0.29192128 58.214
## StateNH 45.28557594 0.17287739 261.952
## StateNJ 48.73236205 0.16476433 295.770
## StateNM 10.27962047 0.20741884 49.560
## StateNY 35.05288069 0.11656630 300.712
## StateNC 14.04629067 0.11845496 118.579
## StateND 8.50272460 0.27661432 30.739
## StateOH 24.36428559 0.12160695 200.353
## StateOK 6.64013387 0.15198470 43.689
## StateOR 25.10135562 0.17147528 146.385
## StatePA 27.77722368 0.11391152 243.849
## StateRI 42.78573215 0.34929794 122.491
## StateSC 6.45313242 0.13772622 46.855
## StateSD 17.40864093 0.27378557 63.585
## StateTN 9.12465574 0.12352173 73.871
## StateTX 19.37322916 0.11446258 169.254
## StateUT 15.58028438 0.24407321 63.834
## StateVT 39.82245044 0.21145812 188.323
## StateVA 17.05781070 0.12901229 132.218
## StateWA 29.05154584 0.14463226 200.865
## StateWV 7.10160304 0.18373240 38.652
## StateWI 31.47504954 0.11974143 262.858
## StateWY 13.10191289 0.33020265 39.678
## DIVISIONMiddle Atlantic NA NA NA
## DIVISIONEast North Central NA NA NA
## DIVISIONWest North Central NA NA NA
## DIVISIONSouth Atlantic NA NA NA
## DIVISIONEast South Central NA NA NA
## DIVISIONWest South Central NA NA NA
## DIVISIONMountain NA NA NA
## DIVISIONPacific NA NA NA
## HouseAcre 0.05660256 0.04121198 1.373
## SaleofAgroProduct 0.32641510 0.01715274 19.030
## Bedrooms 1.43002866 0.02099427 68.115
## RMSP 1.25823651 0.00848897 148.220
## HouseStructureYear1940 to 1949 1.33113790 0.09201083 14.467
## HouseStructureYear1950 to 1959 3.25372416 0.07376821 44.107
## HouseStructureYear1960 to 1969 3.46099137 0.07010690 49.367
## HouseStructureYear1970 to 1979 3.47062261 0.05983415 58.004
## HouseStructureYear1980 to 1989 4.78196106 0.06136985 77.920
## HouseStructureYear1990 to 1999 5.63575289 0.05873099 95.959
## HouseStructureYear2000 to 2004 7.62648117 0.06871434 110.988
## HouseStructureYear2005 8.86172914 0.12278548 72.172
## HouseStructureYear2006 9.18070061 0.12615696 72.772
## HouseStructureYear2007 9.23974146 0.13471073 68.589
## HouseStructureYear2008 9.12946545 0.15132020 60.332
## HouseStructureYear2009 9.05333219 0.17900000 50.577
## HouseStructureYear2010 9.04870387 0.18662216 48.487
## HouseStructureYear2011 9.41093483 0.22761454 41.346
## HouseStructureYear2012 9.33552999 0.22246062 41.965
## HouseStructureYear2013 10.60784753 0.24356779 43.552
## HouseStructureYear2014 10.84192760 0.27293924 39.723
## HouseStructureYear2015 10.69277643 0.31901977 33.518
## HouseStructureYear2016 8.89603288 0.46102680 19.296
## HouseStructureYear2017 7.10709750 0.99109999 7.171
## SINK -0.06339028 0.49832837 -0.127
## Bathtub -1.58510938 0.41452801 -3.824
## Kitchen -1.43115857 0.28369996 -5.045
## INSURANCE 0.00833118 0.00002843 293.064
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## StateAK < 0.0000000000000002 ***
## StateAZ < 0.0000000000000002 ***
## StateAR < 0.0000000000000002 ***
## StateCA < 0.0000000000000002 ***
## StateCO < 0.0000000000000002 ***
## StateCT < 0.0000000000000002 ***
## StateDE < 0.0000000000000002 ***
## StateDC < 0.0000000000000002 ***
## StateFL < 0.0000000000000002 ***
## StateGA < 0.0000000000000002 ***
## StateHI < 0.0000000000000002 ***
## StateID < 0.0000000000000002 ***
## StateIL < 0.0000000000000002 ***
## StateIN < 0.0000000000000002 ***
## StateIA < 0.0000000000000002 ***
## StateKS < 0.0000000000000002 ***
## StateKY < 0.0000000000000002 ***
## StateLA 0.146945
## StateME < 0.0000000000000002 ***
## StateMD < 0.0000000000000002 ***
## StateMA < 0.0000000000000002 ***
## StateMI < 0.0000000000000002 ***
## StateMN < 0.0000000000000002 ***
## StateMS < 0.0000000000000002 ***
## StateMO < 0.0000000000000002 ***
## StateMT < 0.0000000000000002 ***
## StateNE < 0.0000000000000002 ***
## StateNV < 0.0000000000000002 ***
## StateNH < 0.0000000000000002 ***
## StateNJ < 0.0000000000000002 ***
## StateNM < 0.0000000000000002 ***
## StateNY < 0.0000000000000002 ***
## StateNC < 0.0000000000000002 ***
## StateND < 0.0000000000000002 ***
## StateOH < 0.0000000000000002 ***
## StateOK < 0.0000000000000002 ***
## StateOR < 0.0000000000000002 ***
## StatePA < 0.0000000000000002 ***
## StateRI < 0.0000000000000002 ***
## StateSC < 0.0000000000000002 ***
## StateSD < 0.0000000000000002 ***
## StateTN < 0.0000000000000002 ***
## StateTX < 0.0000000000000002 ***
## StateUT < 0.0000000000000002 ***
## StateVT < 0.0000000000000002 ***
## StateVA < 0.0000000000000002 ***
## StateWA < 0.0000000000000002 ***
## StateWV < 0.0000000000000002 ***
## StateWI < 0.0000000000000002 ***
## StateWY < 0.0000000000000002 ***
## DIVISIONMiddle Atlantic NA
## DIVISIONEast North Central NA
## DIVISIONWest North Central NA
## DIVISIONSouth Atlantic NA
## DIVISIONEast South Central NA
## DIVISIONWest South Central NA
## DIVISIONMountain NA
## DIVISIONPacific NA
## HouseAcre 0.169613
## SaleofAgroProduct < 0.0000000000000002 ***
## Bedrooms < 0.0000000000000002 ***
## RMSP < 0.0000000000000002 ***
## HouseStructureYear1940 to 1949 < 0.0000000000000002 ***
## HouseStructureYear1950 to 1959 < 0.0000000000000002 ***
## HouseStructureYear1960 to 1969 < 0.0000000000000002 ***
## HouseStructureYear1970 to 1979 < 0.0000000000000002 ***
## HouseStructureYear1980 to 1989 < 0.0000000000000002 ***
## HouseStructureYear1990 to 1999 < 0.0000000000000002 ***
## HouseStructureYear2000 to 2004 < 0.0000000000000002 ***
## HouseStructureYear2005 < 0.0000000000000002 ***
## HouseStructureYear2006 < 0.0000000000000002 ***
## HouseStructureYear2007 < 0.0000000000000002 ***
## HouseStructureYear2008 < 0.0000000000000002 ***
## HouseStructureYear2009 < 0.0000000000000002 ***
## HouseStructureYear2010 < 0.0000000000000002 ***
## HouseStructureYear2011 < 0.0000000000000002 ***
## HouseStructureYear2012 < 0.0000000000000002 ***
## HouseStructureYear2013 < 0.0000000000000002 ***
## HouseStructureYear2014 < 0.0000000000000002 ***
## HouseStructureYear2015 < 0.0000000000000002 ***
## HouseStructureYear2016 < 0.0000000000000002 ***
## HouseStructureYear2017 0.000000000000746 ***
## SINK 0.898778
## Bathtub 0.000131 ***
## Kitchen 0.000000454531502 ***
## INSURANCE < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.24 on 731544 degrees of freedom
## (4883897 observations deleted due to missingness)
## Multiple R-squared: 0.5073, Adjusted R-squared: 0.5072
## F-statistic: 9656 on 78 and 731544 DF, p-value: < 0.00000000000000022By using train data we can see that accuracy of our model got increased.Moeover, below are some discriptions of summary of model.
Residual Standard Error : It is the average amount that response will deviate from true regression line. In our case actual tax can deviate from true regression line by approximately 13.24.The tax is -12.98 and residual error is 13.24, so our percentage error is 0.26%.
Multiple R-squared : R - squared represents how our model fits the actual data.In our case, the variance is 50% so we can say that some data points will fall near regression and other 50% of data points will be away from regression line. Though we cannot predict exactly that our model will fit our data, however in our case we consider that with 50% of variance we can get predicted model with better accuracy.
Adjusted R- squared : It represents that, as we add on variables into the model, the model gets better and better.
F - statistic : In our case F - statistic value is 9656 is higher than 78, so it suggest that there is relation between predictor and response variable.
##Predicting on test data
pred <- predict(model2, newdata=test)
(combine<-data.frame(cbind(test$Tax, pred)))colnames(combine)<-c("Actual", "Pred") # giving column names
(correlation<-cor.test(combine$Actual,combine$Pred)) #correlation##
## Pearson's product-moment correlation
##
## data: combine$Actual and combine$Pred
## t = 501.2, df = 244206, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.7101197 0.7140298
## sample estimates:
## cor
## 0.7120803The correlation between Actual and predicted variable is 71%, so it depicts that there is a good relationship between response and predicted variable.Moreover, P - value is less than 0.05 so we reject the Null hypothsesis and we reject that there is relation between tax and other factors. Moreover,For instance, from the combined data frame we can say that on value of actual tax is 5 and predicted tax we got is 11.99.
Plot linear model
plot(model2)
Explanation: Residual vs Fitted graph : From the graph we can see that, as red line shows close relation with dashed line in graph, that means it holds reasonably linearity and also there are some outliners which can affect the model.
Normal Q-Q plot : In this graph, we can see that points fits the centre line well and also there are less ouliers which depicts that Q-Q plot is normally distributed.
Scale location: This graph is used to indicate whether spread of points falls near predicted range or not.So, in our case the residuals shows relation in V shape which means that as red line increases residuals comes near it and as it starts decreasing the points go away from red line.
Residuals vs Leverage: This plot helps us to find influential cases.If the point exceeds from cooks distance that is, from dotted line than it shows that there is high leverage or potential for influencing our model if we exclude that point.In our graph, that is not the case, so we can say that there will be no high influence if we exclude outliers point.
Conclusion:
My main aim was to identify price of house on the basis different utilites, but by performing and analysing some codes I realized that accuracy for that model is so less, in which we cannot predict the actual result. So, to overcome this problem I took linear regression model of tax and other factors and measured the tax on different products. By performing that model I came up with 50% accuracy which was not quite enough for me but as by considering other model with less accuracy, I am quite satisfied with tax linear model.Thus, by analysing model I am somewhat confident with my tax prediction model with 50% accuracy. I dont Know why I am getting less accuracy but this is what I tried and what I got by performing different modelling analysis.I also tried to generate maps on basis of states and division but I could not approach to that level, so I mainly focused on ggplots and plots of linear models.
Appendix
Exra code for variable importance and RMSE check
install.packages("Metrics")
library(Metrics)
varImp(model2, scale=FALSE)rmse(combine$Actual, combine$Pred)## [1] NAI was trying to do linear regression of rent and other factors which can affect the overall price of house but because of less accuracy, I tried to make regression of tax and other factors, from which individuals can predict house on basis of tax in differet divisions, states and other utilities. Below are some code which I tried in making linear regression of Rent including other utilites factors.
rent_model <- lm(RENT ~ State+DIVISION+ HouseAcre+ SaleofAgroProduct+
Bathtub+ HotWater+ Bedrooms+ RMSP+ SINK+ Stove+ Toilet+
HouseStructureYear+ Kitchen, data = bind_data)
summary(rent_model)##
## Call:
## lm(formula = RENT ~ State + DIVISION + HouseAcre + SaleofAgroProduct +
## Bathtub + HotWater + Bedrooms + RMSP + SINK + Stove + Toilet +
## HouseStructureYear + Kitchen, data = bind_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1461.56 -220.62 -44.87 169.15 1679.20
##
## Coefficients: (9 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 460.2188 29.7227 15.484
## StateAK 456.4607 22.5039 20.284
## StateAZ 277.5047 12.8022 21.676
## StateAR -21.3679 11.2923 -1.892
## StateCA 568.0293 8.3560 67.978
## StateCO 406.1858 12.4908 32.519
## StateCT 659.9316 14.5749 45.279
## StateDE 322.5243 25.5864 12.605
## StateDC 746.6084 86.9272 8.589
## StateFL 305.9144 9.2477 33.080
## StateGA 132.0896 8.4571 15.619
## StateHI 620.6235 22.3202 27.805
## StateID 151.9215 15.5571 9.765
## StateIL 197.4104 10.5437 18.723
## StateIN 93.5840 10.7059 8.741
## StateIA -6.4183 13.9916 -0.459
## StateKS 34.5243 14.1019 2.448
## StateKY 15.9891 10.5962 1.509
## StateLA 86.5254 11.9707 7.228
## StateME 195.9468 13.8302 14.168
## StateMD 503.2904 12.6861 39.673
## StateMA 574.0597 13.4204 42.775
## StateMI 136.0332 9.3690 14.519
## StateMN 143.4390 10.8887 13.173
## StateMS 22.9586 11.5369 1.990
## StateMO 35.8728 10.1059 3.550
## StateMT 210.4411 15.9646 13.182
## StateNE 1.4889 16.9086 0.088
## StateNV 326.2173 17.3829 18.767
## StateNH 521.6014 15.3580 33.963
## StateNJ 676.9757 13.7059 49.393
## StateNM 184.1733 16.4651 11.186
## StateNY 309.6346 9.2682 33.408
## StateNC 103.5172 8.5782 12.067
## StateND 41.4986 27.3215 1.519
## StateOH 110.4375 9.2568 11.930
## StateOK 29.9802 11.2535 2.664
## StateOR 324.4913 11.5787 28.025
## StatePA 168.6597 8.9594 18.825
## StateRI 570.5102 29.9481 19.050
## StateSC 62.9577 10.1903 6.178
## StateSD -52.5596 22.5691 -2.329
## StateTN 75.9968 9.2880 8.182
## StateTX 213.0187 8.6059 24.753
## StateUT 280.0813 18.9938 14.746
## StateVT 380.8253 17.5987 21.639
## StateVA 265.7977 9.5149 27.935
## StateWA 403.6500 10.2859 39.243
## StateWV 26.5392 16.0326 1.655
## StateWI 121.5722 9.9197 12.256
## StateWY 239.0280 26.6035 8.985
## DIVISIONMiddle Atlantic NA NA NA
## DIVISIONEast North Central NA NA NA
## DIVISIONWest North Central NA NA NA
## DIVISIONSouth Atlantic NA NA NA
## DIVISIONEast South Central NA NA NA
## DIVISIONWest South Central NA NA NA
## DIVISIONMountain NA NA NA
## DIVISIONPacific NA NA NA
## HouseAcre -74.4863 3.2002 -23.276
## SaleofAgroProduct -10.5516 1.4556 -7.249
## Bathtub -135.6574 27.6296 -4.910
## HotWater NA NA NA
## Bedrooms 52.3548 1.6277 32.165
## RMSP 25.9464 0.7963 32.585
## SINK 75.0425 33.2013 2.260
## Stove 7.2099 26.5461 0.272
## Toilet 1.8393 0.2988 6.155
## HouseStructureYear1940 to 1949 14.3280 5.4111 2.648
## HouseStructureYear1950 to 1959 61.7424 4.6436 13.296
## HouseStructureYear1960 to 1969 73.5644 4.6455 15.836
## HouseStructureYear1970 to 1979 72.3659 4.1849 17.292
## HouseStructureYear1980 to 1989 81.6534 4.4012 18.552
## HouseStructureYear1990 to 1999 92.0277 4.3701 21.059
## HouseStructureYear2000 to 2004 128.6929 5.9223 21.730
## HouseStructureYear2005 188.1542 11.2695 16.696
## HouseStructureYear2006 224.8361 11.7077 19.204
## HouseStructureYear2007 199.1017 12.8633 15.478
## HouseStructureYear2008 202.3871 14.2476 14.205
## HouseStructureYear2009 206.7902 17.2536 11.985
## HouseStructureYear2010 194.6655 16.0304 12.144
## HouseStructureYear2011 121.9762 22.8231 5.344
## HouseStructureYear2012 202.4161 22.2270 9.107
## HouseStructureYear2013 195.7962 26.9244 7.272
## HouseStructureYear2014 184.1997 32.4892 5.670
## HouseStructureYear2015 215.4776 37.7444 5.709
## HouseStructureYear2016 188.4295 52.9710 3.557
## HouseStructureYear2017 -15.3768 173.4248 -0.089
## Kitchen -109.1227 24.3165 -4.488
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## StateAK < 0.0000000000000002 ***
## StateAZ < 0.0000000000000002 ***
## StateAR 0.058461 .
## StateCA < 0.0000000000000002 ***
## StateCO < 0.0000000000000002 ***
## StateCT < 0.0000000000000002 ***
## StateDE < 0.0000000000000002 ***
## StateDC < 0.0000000000000002 ***
## StateFL < 0.0000000000000002 ***
## StateGA < 0.0000000000000002 ***
## StateHI < 0.0000000000000002 ***
## StateID < 0.0000000000000002 ***
## StateIL < 0.0000000000000002 ***
## StateIN < 0.0000000000000002 ***
## StateIA 0.646434
## StateKS 0.014359 *
## StateKY 0.131317
## StateLA 0.000000000000493802 ***
## StateME < 0.0000000000000002 ***
## StateMD < 0.0000000000000002 ***
## StateMA < 0.0000000000000002 ***
## StateMI < 0.0000000000000002 ***
## StateMN < 0.0000000000000002 ***
## StateMS 0.046592 *
## StateMO 0.000386 ***
## StateMT < 0.0000000000000002 ***
## StateNE 0.929835
## StateNV < 0.0000000000000002 ***
## StateNH < 0.0000000000000002 ***
## StateNJ < 0.0000000000000002 ***
## StateNM < 0.0000000000000002 ***
## StateNY < 0.0000000000000002 ***
## StateNC < 0.0000000000000002 ***
## StateND 0.128791
## StateOH < 0.0000000000000002 ***
## StateOK 0.007722 **
## StateOR < 0.0000000000000002 ***
## StatePA < 0.0000000000000002 ***
## StateRI < 0.0000000000000002 ***
## StateSC 0.000000000651281176 ***
## StateSD 0.019871 *
## StateTN 0.000000000000000282 ***
## StateTX < 0.0000000000000002 ***
## StateUT < 0.0000000000000002 ***
## StateVT < 0.0000000000000002 ***
## StateVA < 0.0000000000000002 ***
## StateWA < 0.0000000000000002 ***
## StateWV 0.097863 .
## StateWI < 0.0000000000000002 ***
## StateWY < 0.0000000000000002 ***
## DIVISIONMiddle Atlantic NA
## DIVISIONEast North Central NA
## DIVISIONWest North Central NA
## DIVISIONSouth Atlantic NA
## DIVISIONEast South Central NA
## DIVISIONWest South Central NA
## DIVISIONMountain NA
## DIVISIONPacific NA
## HouseAcre < 0.0000000000000002 ***
## SaleofAgroProduct 0.000000000000423541 ***
## Bathtub 0.000000913056005648 ***
## HotWater NA
## Bedrooms < 0.0000000000000002 ***
## RMSP < 0.0000000000000002 ***
## SINK 0.023809 *
## Stove 0.785930
## Toilet 0.000000000752101470 ***
## HouseStructureYear1940 to 1949 0.008101 **
## HouseStructureYear1950 to 1959 < 0.0000000000000002 ***
## HouseStructureYear1960 to 1969 < 0.0000000000000002 ***
## HouseStructureYear1970 to 1979 < 0.0000000000000002 ***
## HouseStructureYear1980 to 1989 < 0.0000000000000002 ***
## HouseStructureYear1990 to 1999 < 0.0000000000000002 ***
## HouseStructureYear2000 to 2004 < 0.0000000000000002 ***
## HouseStructureYear2005 < 0.0000000000000002 ***
## HouseStructureYear2006 < 0.0000000000000002 ***
## HouseStructureYear2007 < 0.0000000000000002 ***
## HouseStructureYear2008 < 0.0000000000000002 ***
## HouseStructureYear2009 < 0.0000000000000002 ***
## HouseStructureYear2010 < 0.0000000000000002 ***
## HouseStructureYear2011 0.000000090935580362 ***
## HouseStructureYear2012 < 0.0000000000000002 ***
## HouseStructureYear2013 0.000000000000356943 ***
## HouseStructureYear2014 0.000000014359983419 ***
## HouseStructureYear2015 0.000000011409434055 ***
## HouseStructureYear2016 0.000375 ***
## HouseStructureYear2017 0.929348
## Kitchen 0.000007212301045274 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 346.5 on 88829 degrees of freedom
## (7398452 observations deleted due to missingness)
## Multiple R-squared: 0.2485, Adjusted R-squared: 0.2478
## F-statistic: 371.8 on 79 and 88829 DF, p-value: < 0.00000000000000022p2 <- predict(rent_model, newdata=test)
(combine<-data.frame(cbind(test$RENT, p2)))colnames(combine)<-c("Actual", "Pred") # giving column names
(correlation<-cor.test(combine$Actual,combine$Pred))##
## Pearson's product-moment correlation
##
## data: combine$Actual and combine$Pred
## t = 86.086, df = 22222, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4901643 0.5098840
## sample estimates:
## cor
## 0.500089The accuracy of Rent model is only 24% and from prediction we can say that by including other utilities such as Bathtub, kitchen, agro products, acres, the rent would be 105.40 whilst our predicted rent is 512, which shows a great difference between actual and predicted value. Thus, lower the accuracy, more worst our prediction would be.